Gaussain Noise in Matlab 1/sqrt(2) (randn(no of bits)+j.*(no of bits))

[aliazmat306]

could somebody please brief me the following method of generating Gaussian Noise specially the term sqrt(2), i.e., why it has been used here

Gaussain Noise in Matlab 1/sqrt(2) (randn(no of bits)+j.*(no of bits))

Thank you very much for your time!

 

[MHanif]

Hi
It is just to keep variance of each sample to be one. randn() function in MATLAB results in a Gaussian noise with zero mean and unit variance. So, variance of randn() + j randn() would be 2 and to keep its variance to be 1 a scaling factor of 1/sqrt(2) is multiplied.

Hope this helps

 

[aliazmat306]

but simple algebra shows that

1/sqrt(2)[1+1] = 1/sqrt(2)

I mean the variance of sum of two independent normal Gaussian Random variable is 2. (Agree)
but when scalar factor (1/sqrt(2)) is multiplied the results is 1/sqrt(2) not 1.
plz explain, I am confused.

 

[MHanif]

Hi
Kindly note that \[var(aX) = a^2 var(X) \]. So, multiplying by \[\frac{1}{\sqrt{2}}\] scales variance by \[\frac{1}{2}\]. Thus total variance is (1+1)/2=1.

 

[aliazmat306]

Thank you very much dear MHanif. This answer is what I wanted.
Thanks Again!!!